I found out how to get it working. All I did was change the sound card type to "sound blaster or compatible", and change the sample rate to the second highest rate (in khz). I did this for Duke Nukem 3D and it worked as well. EXCELLENT!

Yep, that's exactly what I did to get Blood's sound working. Change the sound sample rate down to 22 khz. Obviously, you should always choose sound blaster or compatible since it works for a lot of types of cards.